What is e^{((ipi)/6)} ?

The solution to e^{((ipi)/6)} is (sqrt(3))/2+i 1/2

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simplify e^{((ipi)/6)}

simplify

e^{(\frac{iπ}{6})}

\frac{3}{2} + i \frac{1}{2}

Solution steps

e^{\frac{iπ}{6}}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

= cos (\frac{π}{6}) + i sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{3}{2} + i \frac{1}{2}

\frac{1}{2} i = \frac{i}{2}

= \frac{3}{2} + \frac{i}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 + i}{2}

Rewrite

\frac{3 + i}{2}

in standard complex form:

\frac{3}{2} + \frac{1}{2} i

= \frac{3}{2} + \frac{1}{2} i

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